Rigorous Computing of Dependable/secure Sets of Non-Bias Negative-Sequence Directional Elements

A modern concern in power system protection is that the negative-sequence directional (32Q) element might not differentiate between forward and reverse faults if driven by inverter-based resources (IBRs). To address this concern, one item of subclause 7.2.2.3.4 of the IEEE Standard 2800-2022 specifies the magnitude and angle relationships between the IBR-driven negative-sequence voltage and current. However, a precise analysis has not been posed because the exact dependable and secure regions of a non-bias 32Q element have not been formally determined in a space compatible with the subclause. This paper sets forth an approach to rigorously calculate such exact dependable and secure sets. The proof assistant Isabelle is employed to guarantee correctness. The sets are used to study via EMT simulations the impacts of a specific grid-forming IBR on the 32Q elements in the IEEE 14-bus system.